Physical Climate System

1. At a glance

Earth’s climate is the statistical, long-term behavior of the coupled atmosphere-ocean-land-ice-biosphere system, driven externally by solar input + Earth’s orbital geometry + atmospheric composition, and internally by exchanges of mass + energy + momentum among its components. The thermodynamic state of this system — temperature, humidity, circulation, precipitation, ice volume, ocean stratification, biogeochemical pools — settles into a quasi-equilibrium on timescales from years (ENSO) to millennia (deep-ocean ventilation, ice-sheet response) to millions of years (rock weathering + plate tectonics). Anthropogenic emission of long-lived greenhouse gases since the late 19th century has perturbed this system measurably on every timescale from days (compound extremes) to millennia (committed sea-level rise).

Current state (2024-25, as assessed by NOAA, NASA GISTEMP, HadCRUT5, ERA5, JRA-3Q, Berkeley Earth, and the Copernicus Climate Change Service C3S):

Global mean surface temperature anomaly ~1.55 ± 0.13 °C above the 1850-1900 baseline (calendar year 2024 average, six-dataset mean).
2024 was the first full calendar year above 1.5 °C in the IPCC AR6 reference baseline; 2023 was second-warmest.
Atmospheric CO₂ at Mauna Loa: ~425 ppm (May 2025 monthly mean), ~50 % above the pre-industrial 280 ppm; CH₄ ~1920 ppb (~2.7 × pre-industrial); N₂O ~336 ppb (~1.25 × pre-industrial).
Ocean heat content (0-2000 m) at record-high values (NOAA NCEI, IAP/CAS).
Arctic September sea-ice extent ~13 % per decade decline (NSIDC).
Global mean sea level +24 cm since 1900, accelerating to ~4.6 mm yr⁻¹ in the 2014-2024 satellite altimetry window (Jason-3 + Sentinel-6 Michael Freilich).
Forcing trajectory currently tracks between SSP2-4.5 and SSP3-7.0 (RCP4.5-RCP6.0 in older terminology); aggregated NDCs under the Paris Agreement still imply ~2.5-2.9 °C warming by 2100 (UNEP Emissions Gap 2024).

2. Energy balance + radiation

The first-order driver of Earth’s climate is the imbalance, or near-balance, between absorbed shortwave radiation and emitted longwave radiation at the top of the atmosphere (TOA).

Solar input. The solar irradiance at Earth’s mean orbital distance is the total solar irradiance (TSI) S₀ ≈ 1361 W m⁻² (SORCE, TIM instruments; the value was revised down from the older 1366 W m⁻² in the late 2000s). Because only a disk of area π R² intercepts the parallel beam while the planet has surface area 4 π R², the incoming flux averaged over the globe and the diurnal cycle is S₀ / 4 ≈ 340.25 W m⁻².

Planetary albedo. Of this, a fraction α ≈ 0.30 is reflected — by clouds (~20 %), the surface (~4 %, weighted by snow + ice + desert + ocean angle), and the atmosphere via Rayleigh + aerosol scattering (~6 %). CERES (Clouds and the Earth’s Radiant Energy System) on Terra + Aqua has anchored α near 0.293 since 2000.

Effective radiating temperature. If Earth were a passive grey body in equilibrium and one applied Stefan-Boltzmann (σ = 5.670 × 10⁻⁸ W m⁻² K⁻⁴), the surface temperature required to radiate (S₀ (1 − α) / 4) back to space would be

T_e = ( S₀ (1 − α) / (4 σ) )^(1/4) ≈ 255 K = -18 °C.

Greenhouse effect. The observed global-mean surface temperature is ~288 K (+15 °C), i.e. 33 K warmer than T_e. The difference is the natural greenhouse effect: H₂O, CO₂, CH₄, N₂O, O₃, and clouds absorb outgoing longwave radiation and re-emit a fraction back to the surface, raising the effective emission level into the cold upper troposphere where less longwave can escape.

Radiative forcing. The IPCC defines effective radiative forcing (ERF) as the change in net downward radiative flux at the tropopause (with adjusted stratospheric temperatures and rapid adjustments) due to a perturbation, holding surface temperature fixed. For a doubling of CO₂, ΔF₂×CO₂ ≈ +3.93 W m⁻² (AR6 central estimate; uncertainty ±0.5 W m⁻²) — the AR6 update from the older ~3.7 W m⁻² figure reflects line-by-line radiative transfer recalculations (Etminan et al. 2016; Meinshausen et al. 2020). Total anthropogenic ERF in 2019 was estimated at +2.72 [1.96-3.48] W m⁻² (AR6 Ch.7).

Trenberth-Fasullo-Kiehl energy budget (2009 BAMS; updated 2014, 2023). A canonical depiction of the global-mean budget: 340 W m⁻² in, 240 W m⁻² absorbed (after 100 reflected), surface absorbs ~163, atmosphere absorbs ~77; surface emits ~398 longwave, of which ~342 is absorbed by atmosphere and re-emitted; net surface flux imbalance ~0.7-1.0 W m⁻² (this imbalance, the planetary energy imbalance PEI, is what is driving warming and ocean heat uptake).

3. Greenhouse gases

Carbon dioxide (CO₂). The Mauna Loa Keeling curve has measured atmospheric CO₂ continuously since March 1958 (C.D. Keeling, Scripps; now NOAA GML). The annual-mean rose from 315.97 ppm in 1959 to 421.1 ppm in 2023, and monthly means crossed 425 ppm in May 2024 and again in May 2025. Pre-industrial concentration (Law Dome + Dome C + Vostok ice-core records) was ~278 ppm. CO₂ is responsible for ~ 65-70 % of anthropogenic radiative forcing from well-mixed GHGs. Atmospheric lifetime is multi-modal: a fraction (~20-30 %) persists for >1000 years because of slow uptake by deep ocean and sediments, while ~half is removed within ~century timescales.

Methane (CH₄). Atmospheric concentration ~1920 ppb (2024 NOAA flask network); pre-industrial ~ 700 ppb. Sources: ~40 % wetlands (natural + thawing permafrost), ~30 % agriculture (enteric fermentation in ruminants + rice paddies + manure), ~20 % fossil fuels (oil + gas leakage + coal mines), ~5 % landfills + waste, ~5 % biomass burning. Lifetime in the atmosphere is ~12 years (governed by OH + reactions in the troposphere + minor stratospheric loss). GWP-100 = 28 (AR6 fossil) / 27 (biogenic) without inclusion of carbon-climate feedbacks; GWP-20 = 84 / 81 — methane’s short lifetime makes its near-term impact disproportionate. Methane growth accelerated 2020-23 (the post-COVID “methane surge”; tropical wetlands emissions implicated).

Nitrous oxide (N₂O). ~336 ppb (2024) vs pre-industrial ~270 ppb. Lifetime ~117 years. Sources dominated by agricultural soil management (fertilizer N inputs), animal manure, biomass burning. GWP-100 = 273 (AR6).

Halogenated species (F-gases). Synthetic fluorinated compounds — HFCs (refrigerants), PFCs (semiconductor manufacturing), SF₆ (electrical switchgear), NF₃ (electronics). Trace concentrations but very high GWPs (HFC-23 ~14,600; SF₆ ~25,200). Regulated under the Montreal Protocol’s Kigali Amendment (2016, in force 2019), which schedules an HFC phase-down. CFCs + HCFCs (ozone-depleting + greenhouse) phased out under the Montreal Protocol proper.

Tropospheric ozone (O₃). Short-lived (days-weeks), produced photochemically from NOₓ + VOC + CO precursors. Hemispheric forcing ~+0.4 W m⁻². Background tropospheric O₃ has roughly doubled since pre-industrial.

Water vapor (H₂O). Strongest individual greenhouse gas by absorption fraction (~50 % of clear-sky LW absorption) but a feedback rather than forcing — its atmospheric residence time is ~9 days and its concentration is set by temperature via the Clausius-Clapeyron relation, not by direct human emission (except locally near combustion / cooling towers).

Aerosols. Tropospheric particulates exert a net negative ERF (cooling). AR6 estimates aerosol ERF ~ -1.1 W m⁻² [-1.7 to -0.4] (large uncertainty). Components: sulfate (cooling, formed from SO₂), organic carbon (small cooling), black carbon (warming, +0.1 to +0.2 W m⁻²), nitrate (cooling), dust + sea salt (natural + minor net). Aerosol-cloud interactions (Twomey effect: more CCN → smaller droplets → brighter clouds) are the dominant uncertainty. The 2020 IMO 0.5 % sulfur cap on marine fuels abruptly removed shipping SO₂ over the major shipping lanes, reducing low-cloud reflectivity over the N Atlantic + N Pacific and contributing measurably to the 2023-24 warm anomalies (Quaas et al. 2024; Hansen 2025).

4. Atmospheric structure

The atmosphere stratifies vertically by temperature gradient.

Troposphere (surface to ~9 km at the poles, ~17 km at the equator): T decreases with z at the moist adiabatic lapse rate (~6.5 K km⁻¹ global average); contains ~80 % of atmospheric mass and nearly all water vapor; the seat of weather and the dominant volume for the greenhouse effect.
Stratosphere (tropopause to ~50 km): T increases with z because ozone absorbs solar UV; stably stratified; long mixing times (~years).
Mesosphere (~50-80 km): T decreases again.
Thermosphere (above ~80 km): T increases sharply with z due to absorption of EUV and X-ray.
Tropopause — the inversion separating troposphere from stratosphere; height correlates with surface temperature; the tropopause has risen ~50 m per decade in recent decades (Santer et al. 2003; Lin et al. 2024 — observed via radiosondes + GPS-RO).

The planetary boundary layer (PBL) is the lowest ~0.5-2 km, in direct turbulent exchange with the surface. Its diurnal cycle (deep convective mixed layer by day, shallow stable layer by night) controls surface-atmosphere coupling and pollutant dispersion.

5. General circulation

The atmospheric circulation redistributes ~4 PW of energy from the tropics toward the poles and converts ~2 % of solar input into kinetic energy.

Hadley cells. Thermally direct overturning in each hemisphere from the Intertropical Convergence Zone (ITCZ) (rising near the equator) to the subtropical subsidence at ~30° latitude. The ITCZ migrates seasonally with maximum solar heating. The Hadley cells have been observed to widen poleward ~0.5-1.0° per decade since 1979 (Lu et al. 2007; Staten et al. 2018), with implications for subtropical drying.

Ferrel cells. Indirect (thermally driven against the mean gradient) mid-latitude cells. Dominated by transient baroclinic eddies (extratropical cyclones), which do the actual heat transport.

Polar cells. Weak direct cells in each hemisphere from ~60° to the poles.

Jet streams. Eastward upper-tropospheric wind maxima:

Subtropical jet at ~30°, driven by angular-momentum conservation as Hadley-cell upper branch poleward flow.
Polar (eddy-driven) jet at ~50-60°, driven by baroclinic-eddy momentum convergence.

Both jets meander in Rossby waves with typical zonal wavenumber 4-7. The polar jet’s waviness modulates mid-latitude weather; “stuck” patterns (blocking highs) drive heatwaves (2003 European, 2010 Russian, 2021 Pacific Northwest).

Walker circulation. Pacific zonal overturning: rising motion over the warm-pool (W Pacific Maritime Continent) + Indian Ocean, eastward upper-level flow, sinking over the cold tongue (E Pacific), easterly surface trades. ENSO modulates it: El Niño weakens the Walker cell (warm-pool spreads east); La Niña strengthens it.

Monsoons. Seasonally reversing land-ocean thermal contrast circulations. Major systems: South Asian (Indian), East Asian, West African, North American (NAM), South American (SAM), Australian. Bring 70-80 % of annual rainfall to billions of people in subtropics. AR6: confidence in monsoon precipitation increase under warming (thermodynamic effect, Clausius-Clapeyron) but dynamics (circulation strength) may weaken.

Storm tracks. Zones of high mid-latitude baroclinic activity: N Atlantic (Iceland low region) and N Pacific (Aleutian low region) in the NH; circumpolar SH track around 50-60 °S. Storm tracks have shifted poleward ~1° per decade since 1979 in both hemispheres.

Stratospheric polar vortex (SPV). Wintertime cyclonic vortex over each pole. Sudden Stratospheric Warmings (SSWs) disrupt it ~6 times/decade in NH; subsequent downward propagation of the AO-negative anomaly drives cold-air outbreaks over mid-latitudes (e.g., Feb 2021 Texas winter storm Uri).

6. Ocean circulation

The ocean stores ~1000× the heat capacity of the atmosphere (per unit area, for typical mixed-layer depths) and has absorbed >90 % of the excess energy from anthropogenic forcing since 1971 (AR6 Ch.7; Cheng et al. 2024 update).

Wind-driven surface circulation. Subtropical anticyclonic gyres in each ocean basin (N Atlantic, S Atlantic, N Pacific, S Pacific, Indian) plus subpolar cyclonic gyres. Western boundary currents (Gulf Stream, Kuroshio, Brazil, Agulhas, East Australian) are narrow, fast, deep; eastern boundary currents (Canary, California, Benguela, Humboldt, W Australian) are broad, slow, with coastal upwelling. Sverdrup balance + Stommel + Munk theory establish the boundary intensification.

Thermohaline / Meridional Overturning Circulation (MOC, AMOC). Density-driven (cold + salty → dense) sinking of N Atlantic surface waters at the Greenland-Iceland-Norwegian Seas and the Labrador Sea forms North Atlantic Deep Water (NADW), which spreads southward at depth. Surface return flows from the South Atlantic + Indian Ocean (Agulhas leakage) close the loop. The Southern Ocean’s Antarctic Bottom Water (AABW) sinks around Antarctica (Weddell + Ross Seas). Characteristic strength: ~17 ± 5 Sv (1 Sv = 10⁶ m³ s⁻¹) at 26.5 °N (RAPID-MOCHA array, continuous since 2004).

AMOC trend. Direct RAPID time series shows weakening of ~2-3 Sv between 2004 and 2012, partial recovery thereafter, with high interannual variability. Indirect indices (subpolar gyre SST “warming hole” + Caesar et al. 2018 proxy) suggest a longer-term weakening of ~15 % since mid-20th century. AR6 assessment: AMOC weakening over 21st century is very likely; abrupt collapse before 2100 is assessed as unlikely but with moderate confidence. Ditlevsen + Ditlevsen 2023 Nature Communications argued for a tipping point in 2025-2095 window — viewed by many physical oceanographers as alarmist; subsequent works (Kilbourne et al. 2024) emphasize wide uncertainty.

Ocean heat uptake. The ocean’s mixed layer (~50-150 m typical, deeper in subpolar) absorbs heat on seasonal timescales; mode + intermediate waters (~200-1000 m) sequester it on decadal-multidecadal; deep ocean below ~1500 m, accessed via NADW + AABW formation, on centennial. Argo + Deep Argo programs (~4000 profiling floats; Deep Argo expanding to >6000 m since 2018) provide near-real-time T + S to 2000 m for 65 % of the global ocean.

7. Cryosphere

Greenland Ice Sheet (GrIS). Volume ~2.9 × 10⁶ km³ → sea-level equivalent ~7.4 m. Mass-balance from GRACE (2002-2017) + GRACE-FO (2018-present) + altimetry (ICESat-2, CryoSat-2) + surface mass-balance models (MAR, RACMO, HIRHAM): GrIS lost an average of ~270 ± 50 Gt yr⁻¹ over 2010-2023, equivalent to ~0.75 mm yr⁻¹ of global sea-level rise. The summer 2012 + summer 2019 melt seasons set extreme records; 2024 melt season was high but not record. Surface melt extent maps from MODIS + Sentinel.

Antarctic Ice Sheet (AIS). Volume ~26.5 × 10⁶ km³ → potential SLR ~58 m. East Antarctic Ice Sheet (EAIS) is largest + most stable (cold + above sea level). West Antarctic Ice Sheet (WAIS) is grounded on bedrock below sea level → vulnerable to marine ice-sheet instability (MISI). The Amundsen Sea sector — Pine Island, Thwaites, Smith, Pope glaciers — is losing mass via ocean-driven basal melt of floating ice shelves. Thwaites Glacier (“Doomsday Glacier”) drains ~4 % of WAIS and is the focus of the International Thwaites Glacier Collaboration (ITGC, 2018-2025). AIS mass loss 2010-2023 ~150 ± 100 Gt yr⁻¹.

Sea ice. Arctic September minimum has declined from ~7 × 10⁶ km² (1979-1989 mean) to ~4-5 × 10⁶ km² (2010s-2020s); 2012 set the record low at 3.41 × 10⁶ km². Multiyear ice fraction has fallen from ~60 % to ~30 %, replaced by thinner first-year ice. Antarctic sea ice showed a slight positive trend through ~2014, then collapsed: 2022, 2023, 2024 set successive record lows, several standard deviations below the 1981-2010 baseline. Mechanism still debated (Southern Ocean upper-layer warming + freshwater stratification changes + wind anomalies).

Mountain glaciers + ice caps. ~200,000 worldwide; collectively ~158,000 km³ → ~0.32 m SLR equivalent. Most are losing mass; cumulative contribution to SLR ~0.7 mm yr⁻¹. Particularly rapid loss: Alps, Caucasus, low-latitude Andes, tropical Africa, New Zealand Southern Alps.

Permafrost. Ground that remains ≤ 0 °C for ≥ 2 consecutive years; underlies ~15 % of NH land surface. Stores ~1300-1700 GtC (Hugelius et al. 2014; Schuur et al. 2022), roughly twice the atmospheric carbon stock. Thaw releases CO₂ + CH₄; abrupt thaw (thermokarst) accelerates locally. Estimated emissions ~150-200 GtC by 2100 under SSP3-7.0 (Schuur et al. 2022) — significant for the carbon budget.

Snow cover. NH spring snow-cover extent has declined ~7 % since 1967 (Rutgers Snow Lab + IMS). Earlier snowmelt advances peak streamflow in snow-fed basins (e.g. Western US, HKH).

8. Hydrological cycle

The global water cycle moves ~5 × 10⁵ km³ yr⁻¹ between reservoirs (ocean → atmosphere via evaporation, atmosphere → land + ocean via precipitation, land → ocean via rivers + groundwater).

Clausius-Clapeyron scaling. Saturation vapor pressure obeys dEs/dT ≈ 0.07 Es per K → atmospheric specific humidity increases ~7 % per K of warming if relative humidity is conserved. Observations (HIRS + MSU + AIRS + radiosonde): ~6-7 % K⁻¹ scaling for column water vapor; heavy precipitation extremes scale near or above CC (~7 % per K, sometimes super-CC for sub-daily convective extremes; Westra et al. 2014; Fowler et al. 2024).

Precipitation changes. Mean precipitation responds more slowly than humidity (~2-3 % per K) because evaporation is energy-limited at the surface. Wet-get-wetter, dry-get-drier paradigm holds zonally on average but not regionally. Mediterranean basin, SW North America, parts of southern Africa, Australia drying; tropical convergence zones + high latitudes wetter.

Drought intensification. Compound atmospheric demand (vapor pressure deficit, VPD) + reduced soil moisture → multi-year droughts. SW US 2000-2024 megadrought (Williams et al. 2022) the most severe in ~1200 years per tree-ring reconstructions. Amazon 2023-24 drought tied to El Niño + warming SST.

Streamflow + groundwater. GRACE-FO has revealed regional groundwater depletion in major aquifers (NW India + Punjab, North China Plain, Central Valley California, Saudi Arabia, MENA fossil aquifers) at rates of 5-30 km³ yr⁻¹.

9. Carbon cycle

Fast cycle (years to centuries): atmosphere ↔ ocean (via air-sea CO₂ exchange) ↔ terrestrial biosphere (photosynthesis + respiration + fire). Slow cycle (10⁵-10⁶ yr): rock weathering, sediment burial, vulcanism.

Anthropogenic perturbation (Global Carbon Budget 2024; Friedlingstein et al.). Total emissions ~41.0 GtCO₂ yr⁻¹ in 2024 (37.4 from fossil + cement; 3.6 from net land-use change). Fate of emitted CO₂ over 2014-2023 averages:

Atmosphere: ~48 % (airborne fraction; rose to ~50 % in 2023-24 with weaker land sink)
Ocean: ~26 % (net uptake via solubility pump + biological pump)
Land: ~31 % (net terrestrial biosphere sink; offsets land-use emissions)
Budget imbalance: ~-5 % (statistical residual)

Ocean acidification. Surface ocean pH has fallen from ~8.18 (pre-industrial) to ~8.08 (2024), a 30 % increase in [H⁺]. SSP5-8.5 trajectory implies further ΔpH ≈ -0.3 by 2100. Aragonite + calcite saturation states (Ωar, Ωcalc) decline → harmful to calcifying organisms (corals, pteropods, shellfish). Subpolar + polar surface waters approach undersaturation first.

Land sink variability. Net terrestrial CO₂ uptake fluctuates by ±2 GtC yr⁻¹ year-to-year, dominated by tropical land-flux response to ENSO + drought (large El Niño years → biosphere becomes near-neutral or a source; e.g., 2015-16, 2023). Northern extratropical land (boreal + temperate forests, especially after Pleistocene + LIA recovery) is the most consistent sink. Tropical land is highly variable. Concerns over Amazon source-switch: parts of southeastern Amazon (arc of deforestation + degradation) became a net CO₂ source in the 2010s (Gatti et al. 2021 Nature). 2023-24 Amazon drought further stressed the sink.

Methane budget. Total global emissions ~580 Tg CH₄ yr⁻¹ (Global Methane Budget 2024; Saunois et al.). Of which ~60 % anthropogenic. Imbalance between top-down (atmospheric inversions) and bottom-up (process models + inventories) ~50-100 Tg yr⁻¹. Tropical wetlands the main natural source. MethaneSAT (EDF, launched March 2024) + GHGSat + Sentinel-5P TROPOMI + PRISMA now provide facility-scale to plume-scale methane mapping.

CDR (carbon dioxide removal) overview. Current removals from new pathways (DACCS + BECCS + enhanced weathering + ocean alkalinity) total ~tens of MtCO₂ yr⁻¹ in 2024 — orders of magnitude below the gigatonne scale required for net-zero pathways. AR6 1.5 °C-with-limited-overshoot pathways imply 5-10 GtCO₂ yr⁻¹ CDR by 2050.

10. Climate feedbacks

Feedbacks are processes that, themselves driven by temperature change, modify the radiative imbalance. Defined as λᵢ = dR/dT in W m⁻² K⁻¹ (negative = stabilizing, positive = amplifying).

Feedback	Sign	AR6 Ch.7 value (W m⁻² K⁻¹)	Notes
Planck	strongly −	-3.22 ± 0.04	Blackbody response; reference
Water vapor	+	+1.30 ± 0.12	Clausius-Clapeyron; well-constrained
Lapse rate	−	-0.50 ± 0.20	Tropical upper trop warms more
WV + LR combined	+	+1.15 ± 0.15	Often combined; constant-RH approx
Surface albedo	+	+0.35 ± 0.10	Ice + snow loss
Cloud	+	+0.42 ± 0.36	Largest uncertainty

Cloud feedback decomposition (Zelinka et al. 2020, 2024). Low-cloud cover decreases over subtropical oceans (+, positive); high-cloud altitude rises with warming (+, positive — “fixed anvil temperature” hypothesis, Hartmann + Larson 2002); high-cloud optical depth decreases over extratropics (+ for short-wave but compensating for LW). The net positive cloud feedback in CMIP6 models is supported by observational constraints (Ceppi + Nowack 2021; Myers et al. 2021) using SST patterns.

Non-Planck feedback sum in AR6: +1.42 ± 0.41 W m⁻² K⁻¹ → climate sensitivity parameter S = 1 / (λPlanck + Σλi) ≈ 1 / 1.80 ≈ 0.56 K (W m⁻²)⁻¹ → ECS ≈ 3.93 W m⁻² × 0.56 ≈ 2.2 K minimum; with positive cloud + WV-LR combined the inferred sensitivity is higher.

11. Climate sensitivity

Equilibrium Climate Sensitivity (ECS). The equilibrium surface-temperature rise to doubled atmospheric CO₂, after the climate system has equilibrated (centuries to millennia). Charney 1979 first formalized this concept, giving 1.5-4.5 K based on early GCMs. The IPCC AR1-AR5 retained the 1.5-4.5 K range. AR6 (2021) tightened it:

Best estimate: 3.0 K
Likely range (66 %): 2.5-4.0 K
Very likely range (90 %): 2.0-5.0 K

The tightening came from combining multiple lines of evidence (Sherwood et al. 2020 J. Climate Bayesian synthesis): process-based feedback understanding, instrumental record warming, paleoclimate (LGM, mid-Pliocene), emergent constraints on CMIP6 spread.

Transient Climate Response (TCR). Surface warming at the time of CO₂ doubling under 1 % yr⁻¹ compounding CO₂ increase (year 70). AR6 best 1.8 K [1.4-2.2 K likely]. TCR < ECS because ocean heat uptake delays equilibration.

TCRE (Transient Climate Response to cumulative Emissions). Warming per unit cumulative anthropogenic CO₂ emission. AR6 central estimate 1.65 K per 1000 GtC (= 0.45 K per 1000 GtCO₂) with likely range 1.0-2.3 K per 1000 GtC. TCRE is near-linear in emission, which is the basis of the carbon-budget framing: for a 50 % chance of staying below 1.5 °C, remaining budget from 2020 ≈ 500 GtCO₂; from 2024 ≈ 300 GtCO₂ after subtracting 2020-23 emissions of ~165 GtCO₂. At current ~40 GtCO₂ yr⁻¹ this gives <8 years of “1.5 °C-consistent” emissions.

Earth System Sensitivity (ESS). Includes slow Earth-system feedbacks (ice sheets, vegetation distribution shifts, slow carbon cycle). Paleo-derived ESS ≈ 3-7 K per CO₂ doubling — larger than ECS — relevant on multi-millennial timescales.

12. Internal variability

Even with constant forcing, the coupled atmosphere-ocean system generates internal variability across timescales.

ENSO (El Niño-Southern Oscillation). Coupled tropical Pacific mode; period 2-7 yr; phases El Niño (warm cold-tongue, weakened Walker, Nino-3.4 SST anomaly > +0.5 K for ≥5 months) and La Niña (opposite). Strong El Niño years (1982-83, 1997-98, 2015-16, 2023-24) bring global temperature anomaly +0.1 to +0.2 K above background, reorganize global precipitation. 2023-24 El Niño was a strong event that decayed in spring 2024; transitioned to La Niña late 2024-2025.

Pacific Decadal Oscillation (PDO) / Interdecadal Pacific Oscillation (IPO). Multi-decadal pattern of N Pacific SST. PDO+ phase favors more frequent El Niño-like states. 1976-77 PDO regime shift coincided with global temperature acceleration.

Atlantic Multidecadal Oscillation/Variability (AMO/AMV). Basin-scale N Atlantic SST mode; period ~60-80 years. Modulates Sahel rainfall, Atlantic hurricane activity, European summer temperatures.

North Atlantic Oscillation (NAO) / Arctic Oscillation (AO). Northern Hemisphere annular modes; control winter storm tracks + temperatures over Europe + E NA. Positive NAO → mild wet NW Europe, dry Mediterranean.

Southern Annular Mode (SAM). SH analog; positive SAM trend in recent decades linked to ozone hole + GHG forcing → poleward shift of SH westerlies.

Madden-Julian Oscillation (MJO). 30-90 day eastward-propagating tropical convective + circulation envelope; main source of subseasonal predictability in tropics.

13. Climate models

The climate-model hierarchy spans simple to comprehensive:

EBM (Energy Balance Model). Zero- or one-dimensional radiative-convective or latitudinally-resolved energy balance. Useful for sensitivity intuition.
RCM (Radiative-Convective Model). Vertically resolved, no horizontal dynamics. Manabe + Wetherald 1967 J. Atmos. Sci. — the foundational calculation showing CO₂ doubling → ~2 K warming with humidity feedback. Cornerstone reference.
EMIC (Earth-system Model of Intermediate Complexity). Coarse-resolution, fast; used for multi-millennial paleoclimate + carbon-cycle experiments (UVic, Bern3D-LPX, LOVECLIM, CLIMBER).
AGCM / OGCM. Atmosphere-only / ocean-only general circulation models.
AOGCM (coupled GCM). Atmosphere-ocean coupled.
ESM (Earth System Model). AOGCM + interactive carbon cycle + dynamic vegetation + atmospheric chemistry + interactive ice sheets (some) + nitrogen cycle.

CMIP — Coupled Model Intercomparison Project. Multi-model coordinated experiments under the WCRP. CMIP6 (2018-2023) underpinned IPCC AR6, ~50 model groups, ~100 model variants; standard experiments DECK + scenario MIP (ScenarioMIP, with SSP1-1.9 / SSP1-2.6 / SSP2-4.5 / SSP3-7.0 / SSP5-8.5). CMIP7 in development; experiments + first runs expected through 2026-27, contributing to AR7 (~2028-30).

Major modeling centers + flagship models.

NCAR CESM (US): Community Earth System Model. CESM2 (atmospheric component CAM6) in CMIP6; CESM3 in development. CESM Large Ensemble (CESM2-LE, 100 members) widely used for internal-variability vs forced-response separation.
GFDL (NOAA): CM4 (climate model) + ESM4 (Earth system) + SPEAR (seamless prediction).
GISS (NASA): ModelE / GISS-E2.1, GISS-E2-2-G; long heritage going back to Hansen 1981.
UKMO Hadley Centre (UK): HadGEM3 (climate) + UKESM1 (Earth system).
EC-Earth (European consortium): EC-Earth3, multiple configurations.
CNRM (France): CNRM-CM6, CNRM-ESM2.
IPSL (France): IPSL-CM6A-LR.
MPI-M (Germany): MPI-ESM1.2 (LR + HR); ICON-ESM in development.
CSIRO (Australia): ACCESS-CM2 + ACCESS-ESM1.5.
NorESM (Norway): NorESM2-LM + NorESM2-MM.
CMCC (Italy): CMCC-CM2-SR5, CMCC-ESM2.
JAMSTEC + AORI + NIES (Japan): MIROC6, MIROC-ES2L.
MRI (Japan): MRI-ESM2.
BCC + CAS (China): BCC-CSM2-MR, CAS FGOALS-g3, CAS FGOALS-f3.
CanESM5 (Canada).

Horizontal resolution. CMIP6 atmospheric resolution typically ~100-200 km; ocean ~25-100 km. CMIP6 HighResMIP (~25-50 km atmosphere, ~10-25 km ocean) showed substantial improvement in storm tracks, blocking, tropical cyclones, eddy fluxes.

Storm-resolving + km-scale global models. A new generation of storm-resolving global models (SRGM) runs at ≤ 5 km horizontal grid spacing, partially resolving deep convection without parameterization. Initiatives: DYAMOND-1/2/3 (DYnamics of the Atmospheric General Circulation Modeled On Non-hydrostatic Domains) intercomparison; models include NICAM (Japan, icosahedral), MPAS (US/NCAR, voronoi), GEOS (NASA cubed-sphere), IFS (ECMWF), ICON (Germany), X-SHiELD (NOAA/GFDL/Vulcan), E3SM-MMF (US DOE multiscale modeling). The EVE — EERIE + nextGEMS EU initiatives push toward km-scale climate runs (2024-26).

Regional climate models (RCMs). Higher-resolution (1-25 km) dynamical downscaling. Major frameworks: WRF (NCAR), WRF-ARW + WRF-Climate, RegCM (ICTP), CCLM (COSMO consortium), RACMO + HIRHAM (polar), BARRA / BARPA (BOM Australia), NARCCAP + CORDEX intercomparisons. CMIP6-driven CORDEX-CMIP6 beginning to deliver outputs 2024-26.

14. AI for climate + weather (2024-26 state)

Foundation-style ML models have leapt to or past dynamical NWP skill for medium-range weather, at orders-of-magnitude lower inference cost.

GraphCast (Lam et al. 2023 Science; Google DeepMind). Graph neural network on 0.25° icosahedral grid, ~36 million params, 10-day forecast in ~60 s on a single TPU v4. Outperforms ECMWF HRES on 90 % of 1380 verification targets.
Pangu-Weather (Bi et al. 2023 Nature; Huawei Cloud). 3D Earth-specific transformer; hierarchical model trained at 4 lead times (1, 3, 6, 24 h). State-of-the-art among ML models on tropical-cyclone tracking when published.
FourCastNet (Pathak et al. 2022; NVIDIA). Adaptive Fourier Neural Operator (AFNO) on 0.25° grid; FourCastNet-v2 (SFNO, spherical Fourier neural operator; Bonev et al. 2023).
GenCast (Price et al. 2024 Nature; Google DeepMind). Diffusion-based ensemble weather model on 0.25°; 50-member ensemble in minutes; outperforms ECMWF ENS on ~97 % of targets.
AIFS (ECMWF Artificial Intelligence/Integrated Forecasting System; Lang et al. 2024). Graph transformer; operational at ECMWF since Feb 2025 alongside dynamical IFS.
NeuralGCM (Kochkov et al. 2024 Nature; Google Research + ECMWF). Differentiable atmospheric GCM (dynamical core) + ML parameterization layer. Hybrid approach — preserves physical consistency while learning sub-grid closures. Demonstrates skill on climate timescales (decade-length runs).
Stormer (Nguyen et al. 2024; Microsoft / UCLA). Vision-transformer for medium-range.
AURORA (Microsoft 2024). Foundation model trained on 1M+ hours of meteorological + environmental data; transfers to multiple downstream tasks (air quality, ocean waves, hurricanes).
ClimaX (Nguyen et al. 2023; Microsoft). Generalist climate-weather foundation transformer; pre-trained on CMIP6 + ERA5.
ACE (Watt-Meyer et al. 2023; AI2). AI Climate Emulator; emulates SHiELD atmosphere at 100× speedup.

Caveats. ML weather models inherit ERA5 biases; their behavior under out-of-distribution climate (warmer than training distribution) is uncertain — a hard problem for climate-projection use. Hybrid approaches (NeuralGCM) and physics-conserving designs aim to extend ML to climate timescales. Energy-cycle conservation + mass conservation are not guaranteed by pure data-driven methods.

Downscaling + bias correction. Super-resolution ML (Vandal et al. DeepSD; Stengel et al. 2020; Harder et al. 2024) and generative models (cGAN, diffusion) for statistical downscaling of GCM output to regional grids.

Subseasonal-to-seasonal (S2S). ML ensembles are closing the skill gap in the 2-6 week range where dynamical models historically struggle.

Methane plume detection. Carbon Mapper + EDF MethaneSAT + GHGSat operationally combine satellite imagery with ML for facility-scale emission quantification.

15. Observation systems

Surface station networks. GHCN (Global Historical Climatology Network) — daily + monthly. WMO ~11,000 stations. National services: NOAA + NWS, Met Office, DWD, JMA, BoM, ECCC, INMET. ISD (Integrated Surface Database) and HadISD for sub-daily. GTS (Global Telecommunication System) distributes real-time obs.

Ocean.

Argo program (started 2000): >4000 profiling floats, T + S to 2000 m every 10 days; Deep Argo to 6000 m expanding.
GO-SHIP repeat hydrography sections.
OceanSITES moorings (RAPID, OSNAP, TAO/TRITON, RAMA, PIRATA, NOG).
Sea-surface T blends: NOAA OISST, OSTIA, ESA SST-CCI.
Sea-level: tide gauges (PSMSL) + satellite altimeters (TOPEX/Poseidon 1992-2005, Jason-1/2/3, Sentinel-6 Michael Freilich since 2020, SWOT since Dec 2022 — wide-swath KaRIn altimeter).

Cryosphere.

ICESat-2 (NASA, 2018-): ATLAS photon-counting laser altimeter for ice + sea-ice freeboard + canopy.
CryoSat-2 (ESA, 2010-): SIRAL radar altimeter for ice freeboard + thickness.
GRACE / GRACE-FO (NASA + DLR/GFZ 2002-17 / 2018-): gravity-based mass-change of ice sheets + groundwater.
Sentinel-1 SAR for ice motion + interferometry.
MODIS / VIIRS / Sentinel-3 SLSTR for snow + ice surface temperature + extent.

Atmosphere — composition.

OCO-2 + OCO-3 (NASA, 2014/2019): column CO₂ from solar reflected NIR.
GOSAT + GOSAT-2 (JAXA, 2009/2018): column CO₂ + CH₄.
TROPOMI on Sentinel-5P (ESA 2017): high-res NO₂, CH₄, CO, O₃, SO₂.
MethaneSAT (EDF/NMS, March 2024): targeted high-res methane mapping of oil + gas regions.
GHGSat (commercial, Canada): facility-scale CH₄ plumes.
MERLIN (DLR/CNES, 2025 launch): pulsed-DIAL LIDAR for CH₄.
EarthCARE (ESA/JAXA, May 2024): cloud + aerosol active sensing (94 GHz CPR + ATLID lidar + MSI imager + BBR radiometer).
AIRS, IASI, CrIS hyperspectral IR sounders.
TCCON (Total Carbon Column Observing Network): ground-based FTIR validation network.

Atmosphere — dynamics + state.

Geostationary: GOES-16/18 (NOAA), Himawari-9 (JMA), Meteosat-9/10/11 + MTG-I1 (EUMETSAT), GK-2A (KMA), FY-4 (CMA).
Polar-orbiting: NOAA-20/21 + JPSS series, MetOp-A/B/C + MetOp-SG, Suomi NPP.
Aeolus (ESA 2018-2023): first space-borne wind LIDAR; demonstrated value for global wind sampling.
TRMM / GPM (NASA/JAXA): precipitation radars.

Reanalyses. Combine forecast models with all available observations to produce dynamically + thermodynamically consistent gridded retrospective records.

ERA5 (ECMWF, 0.25°, 1940-present hourly): the de-facto standard global reanalysis.
ERA5-Land (9 km, surface variables).
MERRA-2 (NASA, 0.5° × 0.625°, 1980-present).
JRA-55 (JMA, 1958-2023); JRA-3Q (JMA, 1947-present, replacement, released 2024).
NCEP-CFSR (NOAA, 1979-present).
20CR (Twentieth Century Reanalysis, 1836-present, surface-pressure only).
Regional reanalyses: CERRA (Copernicus European Regional ReAnalysis, 11 km Europe), BARRA-R2 (Australia), NARR (N America).

16. AR6 and AR7

IPCC AR6 (2021-2023). Three Working Group reports + a Synthesis:

WG1: Physical Science Basis — published Aug 2021. Headline: “It is unequivocal that human influence has warmed the atmosphere, ocean and land. Widespread and rapid changes … have occurred.” 1.5 °C remaining carbon budget (50 % chance from 2020) ≈ 500 GtCO₂; (67 %) ≈ 400 GtCO₂.
WG2: Impacts, Adaptation, Vulnerability — Feb 2022. Loss + damage prominent; adaptation limits at higher warming; ~3.3-3.6 B people in highly vulnerable contexts.
WG3: Mitigation — April 2022. Net-zero CO₂ by ~2050 needed for 1.5 °C with limited overshoot; rapid + deep cuts in all sectors; demand-side measures account for 40-70 % reduction potential.
AR6 Synthesis Report (SYR) — March 2023.

AR6 Special Reports (preceding WG1):

SR15 (Oct 2018): Global Warming of 1.5 °C.
SROCC (Sept 2019): Ocean and Cryosphere.
SRCCL (Aug 2019): Climate Change and Land.

AR7 cycle (2023-2030). Bureau elected July 2023. AR7 cycle plan agreed Jan 2024. Methodology Report on Short-Lived Climate Forcers (2027). Special Report on Cities (2027). WG reports + Synthesis 2028-2030 expected. AR7 WG1 likely 2028-2029; will incorporate CMIP7, new attribution methodologies, possibly km-scale modeling contributions, expanded ML evaluation.

17. Observed changes

Comprehensive Indicators of Climate Change (IGCC; Forster et al. 2024, updated annually):

Global mean surface temperature: +1.43 K (2014-2023 decade-mean vs 1850-1900) → 2024 single-year +1.55 K.
Ocean heat content (0-2000 m): rising ~0.5-0.7 ZJ yr⁻¹ in 2010s, ~1.0 ZJ yr⁻¹ in 2020s.
Sea level: +24 cm since 1900; satellite-era rate 1993-2014 ~3.0 mm yr⁻¹ → 2014-2024 ~4.6 mm yr⁻¹ (acceleration significant).
Arctic sea ice extent: September -13 % per decade; March -2.6 % per decade.
Greenland mass loss: -270 ± 50 Gt yr⁻¹ (2010-2023).
Antarctic mass loss: -150 ± 100 Gt yr⁻¹ (2010-2023).
Mountain glacier mass loss: -300 to -400 Gt yr⁻¹ globally (2010-2023; Hugonnet et al. 2021 + updates).
NH spring snow cover: -7 % since 1967.
Atmospheric water vapor: +1.0 % per decade (HIRS + radiosonde).
Extreme heat days: 5 × increase in heatwaves over 1 °C warmer climate vs 1850-1900 (Perkins-Kirkpatrick + Lewis 2020).
Heavy precipitation events: increased frequency in most continental regions (AR6 WG1 Ch.11 high confidence).
Compound + cascading events: heatwave + drought + wildfire (2020 W US, 2023 Canada wildfires record 18.4 M ha burned, 2023 Hawaii Lahaina fire), wet-bulb extremes (Pakistan + Persian Gulf summer).

18. Detection + attribution

Formal detection-attribution. Optimal fingerprinting (Hasselmann 1993, 1997; Allen + Tett 1999; Ribes et al. 2017) regresses observed change onto model-simulated forced “fingerprints” while accounting for internal variability. AR6 WG1 Ch.3 concludes:

The observed +1.07 K warming over 1850-1900 to 2010-2019 is attributed entirely to human activities: GHGs contribute +1.0 to +2.0 K, offset by aerosols -0.0 to -0.8 K, with very small natural (solar + volcanic) contribution.
Human influence is virtually certain to have caused observed warming.

Extreme-event attribution. Risk-based framing: how does anthropogenic forcing change the probability or intensity of a specific event? Two approaches:

Probabilistic (Stott et al. 2004): fraction of attributable risk FAR = 1 - (P0 / P1).
Storyline / boundary-conditions: fix circulation, compare thermodynamic state.

World Weather Attribution (WWA) (collaboration; Otto, van Oldenborgh, Vautard, Philip, Kew, Clarke et al.) routinely delivers rapid attribution within 1-3 weeks of major events: 2021 Pacific NW heatdome (PNW 2021) “virtually impossible without climate change” (~1-in-1000-yr today, but ~150 × more likely than pre-industrial); 2022 Pakistan floods; 2023 Mediterranean wildfires; 2024 Hurricane Helene rainfall.

ClimaMeter (CNRS + IPSL, 2023+) provides operational rapid analog-based attribution.

19. Tipping points + abrupt change

A tipping element is a sub-system of the Earth system that can undergo qualitative state change at a threshold. Lenton + Held + Schellnhuber 2008 PNAS introduced the climate tipping-element framework. Armstrong McKay et al. 2022 Science updated assessments with thresholds + warming levels:

Element	Threshold (likely range)	Time-scale to threshold
GrIS collapse	~1.5 K (0.8-3.0)	1000-15,000 yr
WAIS collapse	~1.5 K (1.0-3.0)	~2000 yr
Labrador-Irminger Sea convection	~1.8 K (1.1-3.8)	decades
AMOC collapse	~4 K (1.4-8.0)	~50-300 yr
Amazon dieback	~3.5 K (2.0-6.0)	~100 yr
Boreal forest northward + dieback	~4 K	~50-100 yr
Permafrost abrupt thaw	~1.5 K	decades
Arctic winter sea ice	~6.3 K	~20 yr
Mountain glaciers	~2 K	~200 yr
Coral reefs (low-latitude)	~1.5 K	~10 yr
West African monsoon shift	~2 K	~10 yr
Sahel + W African veg	~2 K (also wettening)	~50-200 yr
Barents Sea sea-ice	?	~25 yr

The headline message: exceeding 1.5 °C significantly elevates the risk of several tipping events, and warming above 2 K crosses multiple element thresholds with potential cascading interactions (Wunderling et al. 2021, 2024). “Hothouse Earth” pathways (Steffen et al. 2018) describe these cascades qualitatively.

20. Mitigation pathways

Integrated Assessment Models (IAMs). Couple energy + economy + land + climate. Two model families:

Cost-benefit IAMs: DICE/RICE (Nordhaus), FUND (Tol), PAGE (Hope). Optimize welfare with explicit damage function.
Cost-effectiveness / process IAMs: GCAM (PNNL/JGCRI), MESSAGE-GLOBIOM (IIASA), REMIND-MAgPIE (PIK), IMAGE (PBL), AIM (NIES), WITCH (FEEM), POLES (JRC). Detailed energy + land sectors; minimize cost of meeting a climate target.

SSP-RCP scenarios (Riahi et al. 2017; O’Neill et al. 2017): five socioeconomic SSPs × radiative-forcing RCPs. AR6 ScenarioMIP uses SSP1-1.9, SSP1-2.6, SSP2-4.5, SSP3-7.0, SSP5-8.5.

1.5 °C pathways. AR6 WG3 C.1.2: limited or no overshoot pathways require global GHG emissions to peak before 2025, decline 43 % by 2030 (vs 2019), 84 % by 2050; net-zero CO₂ around 2050; net-zero all-GHG around 2070.

Current trajectory. UNEP Emissions Gap Report 2024: unconditional NDCs lead to ~2.6 °C; conditional NDCs ~2.5 °C; current policies ~3.1 °C; a 1.5 °C-aligned pathway demands a 42 % reduction by 2030 from 2019 levels — gap is ~25-31 GtCO₂e in 2030.

Sectoral levers. Electricity (renewables + storage + grid + nuclear + CCS); transport (EVs + biofuels + e-fuels + modal shift); buildings (heat pumps + retrofit + electrification); industry (electrification + H₂ + CCS + circular); agriculture + land (methane + N₂O + land carbon); CDR (BECCS, DACCS, enhanced weathering, ocean alkalinity, biochar, reforestation).

21. 2024-25 state of climate (snapshot)

2024 GMST: +1.55 ± 0.13 K above 1850-1900 (six-dataset mean); first calendar year above the 1.5 K threshold. 2023 was +1.45 K. The 2023-24 record warmth exceeded what underlying GHG trend + ENSO alone could explain by ~0.2 K; candidate explanations: (a) IMO 2020 shipping aerosol reduction (-SO₂ → -low-cloud albedo over shipping lanes; Hansen 2025; Quaas et al. 2024), (b) Hunga Tonga-Hunga Ha’apai Jan 2022 stratospheric water-vapor injection (~150 Tg H₂O; Millán et al. 2022; ~+0.04 K transient surface effect estimated), (c) solar cycle 25 max in 2024, (d) reduced biomass-burning aerosol from improved fire management in some regions, (e) deep-ocean / circulation rearrangement amplifying surface heat uptake.
Atmospheric composition (2024-25): CO₂ ~425 ppm (May 2025 ML monthly mean), CH₄ ~1920 ppb, N₂O ~336 ppb.
Ocean heat content (0-2000 m): 2024 set new record (NOAA NCEI; IAP/CAS — Cheng et al. 2025); cumulative heat uptake since 1971 ~ 396 ZJ.
Sea level: 2024 annual rise ~5 mm (Copernicus C3S); 2014-2024 trend ~4.6 mm yr⁻¹, vs 1993-2014 ~3.0 mm yr⁻¹. NASA + ESA released coordinated 2024 statement on accelerating SLR.
Arctic + Antarctic sea ice: 2024 Arctic Sept extent 4.28 M km² (sixth-lowest); Antarctic Feb 2024 extent record-low for second consecutive year.
2024 Atlantic hurricane season: 18 named storms, 11 hurricanes, 5 majors. Hurricane Beryl became Cat 5 in early July — earliest Cat 5 on record in the Atlantic basin. Helene (late Sept) caused catastrophic flooding in Appalachia (Asheville NC). Milton intensified from TS to Cat 5 in 24 h (rapid intensification linked to record-warm Gulf of Mexico SST).
North America wildfire: 2023 Canada all-time record 18.4 M ha burned; 2024 ~5 M ha — high but down from 2023; California 2025 January Palisades + Eaton fires in Los Angeles destroyed >10,000 structures.
Compound + cascading events: 2024 Asia heatwave (S Asia + SE Asia April-June; Philippines + Bangkok records); 2024 Sahel + Niger flooding (Aug-Sept).

21b. Governing equations + numerics (primer)

A modern AOGCM / ESM integrates a coupled system whose atmospheric component solves a flux form of the primitive equations on the rotating sphere — the Navier-Stokes momentum equations with the hydrostatic approximation, continuity, the first law of thermodynamics, and a transport equation for every prognostic tracer (specific humidity, cloud water/ice, aerosol species, chemical species, carbon-cycle tracers in ESMs).

Atmospheric primitive equations (hydrostatic, σ or hybrid p-σ vertical coordinate):

Momentum (vector): ∂v/∂t + (v·∇)v + f k × v = -(1/ρ) ∇p + g + F_fric
Hydrostatic balance: ∂p/∂z = -ρ g
Continuity: ∂ρ/∂t + ∇·(ρ v) = 0
Thermodynamics: cp DT/Dt - α Dp/Dt = Q_diabatic
Water vapor transport: Dq/Dt = E - P + diffusion
State (ideal gas): p = ρ R T_v

Non-hydrostatic dynamics. Storm-resolving models (≤ 5 km grid spacing) abandon hydrostatic balance and integrate fully compressible Euler equations (e.g., ICON-NH, MPAS-A, WRF-ARW, NICAM, GEM). At these scales deep moist convection is partially resolved → eliminates the largest single source of parameterization uncertainty (the cumulus scheme).

Spatial discretization.

Spectral transform (Eulerian or semi-Lagrangian): spherical harmonics for horizontal — historically dominant (IFS, GFS, prior CESM with finite-volume FV). High accuracy but communication-heavy at exascale.
Finite-volume on cubed-sphere (FV3 at GFDL + NOAA → operational GFS since 2019, also used by E3SM-EAM, GEOS).
Finite-element / spectral-element on cubed-sphere (HOMME → CAM-SE, E3SM-EAM at higher resolution).
Icosahedral / hexagonal / Voronoi tessellation (NICAM, ICON, MPAS) — uniform-area cells, no polar singularity.

Time stepping. Split-explicit or semi-implicit semi-Lagrangian (SISL, ECMWF IFS). Tracer transport often by Lin + Rood 1996 monotonic flux-form scheme or MPDATA (Smolarkiewicz).

Sub-grid parameterizations. Convection (Tiedtke, Zhang-McFarlane, Bechtold), boundary-layer turbulence (Mellor-Yamada, EDMF, CLUBB, TKE), cloud microphysics (single- to triple-moment bulk; Morrison, Thompson, P3), radiation (RRTMG → RRTMGP), gravity waves (orographic + non-orographic), surface (land-surface models CLM, JULES, ORCHIDEE, NOAH-MP, MOSES). These are the principal source of inter-model spread.

Ocean components. Hydrostatic Boussinesq primitive equations on z, σ, or hybrid vertical coordinate.

MOM (Modular Ocean Model, GFDL) → MOM6 in CMIP6.
NEMO (European consortium).
POP / MOM6 in CESM2 + CESM3.
HYCOM (Navy + NOAA, hybrid coordinate).
MITgcm.
OPA legacy.

Sea ice. Multi-category thickness distributions (Thorndike-Bitz); rheology Hibler 1979 elastic-viscous-plastic or recent elasto-brittle (neXtSIM). Components: CICE (LANL → CESM, ACCESS), SI3 (NEMO), GSI (MOM6).

Coupling. Coupler exchanges fluxes between components: CPL7 / MCT / cmeps (CESM/E3SM), OASIS3-MCT (European), NUOPC (NOAA).

Numerical methods literature. Durran 2010 Numerical Methods for Fluid Dynamics; Lauritzen et al. 2011 Numerical Techniques for Global Atmospheric Models; Williamson 2007 J. Comput. Phys. dynamical-core review.

22. Software + tools

Python climate analysis ecosystem.

Xarray — labeled n-dimensional arrays; cornerstone library; integrates NetCDF + Zarr + HDF5.
Dask — parallel + out-of-core arrays + scheduler; backs Xarray on large data.
Pangeo — community framework: Xarray + Dask + Jupyter + cloud-native Zarr in object storage. Major Pangeo cloud deployments on AWS, GCP, Azure, NASA Veda, ESA-CCI Open Data Portal.
Iris — Met Office Python library; cube-based; ESMValTool foundation.
ESMValTool / ESMValCore — community evaluation framework for CMIP outputs.
CDO (Climate Data Operators, MPI-M) + NCO (NetCDF Operators) + NCL (NCAR Command Language, retired but in use).
MetPy (Unidata) for meteorological calculations + plotting.
Cartopy for geo-referenced plotting.
GeoCAT (NCAR migration from NCL).
xclim for climate indices.
WRF-Python + wrf-python.
climlab (Brian Rose) — pedagogical EBM + RCM + GCM-light in Python.

Visualization. Panoply (NASA GISS) for NetCDF browsing; Ferret (NOAA PMEL) legacy; Met Office Cylc workflow engine.

AI-weather model code. GraphCast, Pangu-Weather, FourCastNet, ClimaX, ACE all have public training + inference code on GitHub. NeuralGCM released under Apache 2 by Google Research. AIFS weights released by ECMWF for non-commercial research.

Community models. CESM (BSD; full distribution + tutorials), WRF (open), MPAS-A (open), E3SM (open), ICON (Apache 2.0 since 2024).

23. Cross-references

[[ClimateScience/_index]] — library overview.
[[Engineering/environmental-engineering]] — air + water quality, environmental remediation.
[[Engineering/Tier3/photovoltaic-cells]] — solar PV physics + technology.
[[Engineering/Tier3/wind-turbine-types]] — wind turbine classes + economics.
[[Engineering/Tier3/battery-chemistries]] — Li-ion, LFP, solid-state, flow.
[[Engineering/Tier3/energy-storage-systems]] — grid storage technologies.
[[Engineering/Tier3/hydrogen-fuel-cells]] — green H₂ + fuel-cell chemistry.
[[Engineering/Tier3/heat-pumps]] — building + industrial electrification.
[[Engineering/Tier3/nuclear-reactor-types]] — fission options for low-C electricity.
[[Engineering/Tier3/refrigerants]] — Montreal + Kigali compliance, low-GWP HFOs.
[[EnergyMarkets/electricity-markets]] — wholesale markets, capacity expansion, carbon-aware dispatch.
[[EnergyMarkets/_index]] — energy-market library.
[[Economics/microeconomics-foundations]] — externalities, Pigouvian carbon pricing, public goods, discounting.
[[Math/ode-numerical-methods]] — climate-model time stepping, explicit + implicit + IMEX schemes.
[[Math/pde-methods]] — finite-difference / finite-volume / spectral / spectral-element methods for atmospheric + ocean primitive equations.
[[Compute/transformer-architecture]] — substrate for ML weather + climate models (GraphCast, Pangu, AIFS, NeuralGCM).

24. Citations + canonical references

IPCC (consensus).

IPCC AR6 WG1 The Physical Science Basis (2021).
IPCC AR6 WG2 Impacts, Adaptation, and Vulnerability (2022).
IPCC AR6 WG3 Mitigation of Climate Change (2022).
IPCC AR6 Synthesis Report (2023).
IPCC SR15 Global Warming of 1.5 °C (2018).
IPCC SROCC Ocean and Cryosphere (2019).
IPCC SRCCL Climate Change and Land (2019).

Foundational physics + modeling.

Manabe S, Wetherald RT. 1967. Thermal equilibrium of the atmosphere with a given distribution of relative humidity. J. Atmos. Sci. 24: 241-259. (First quantitative CO₂-doubling sensitivity ~2 K.)
Charney JG et al. 1979. Carbon Dioxide and Climate: A Scientific Assessment. NAS. (1.5-4.5 K range, established for 40 yr.)
Hansen J et al. 1981. Climate impact of increasing atmospheric carbon dioxide. Science 213: 957-966.
Trenberth KE, Fasullo JT, Kiehl J. 2009. Earth’s global energy budget. Bull. Amer. Meteor. Soc. 90: 311-323.
Wallace JM, Hobbs PV. 2006. Atmospheric Science: An Introductory Survey, 2nd ed. Academic Press.
Hartmann DL. 2015. Global Physical Climatology, 2nd ed. Elsevier.
Solomon S. 2007. Climate Change Science.
Pierrehumbert RT. 2010. Principles of Planetary Climate. Cambridge University Press.
Holton JR, Hakim GJ. 2012. Introduction to Dynamic Meteorology, 5th ed.

Climate sensitivity + feedback.

Sherwood SC et al. 2020. An assessment of Earth’s climate sensitivity using multiple lines of evidence. Rev. Geophys. 58: e2019RG000678. (Foundation of AR6 ECS range.)
Zelinka MD et al. 2020. Causes of higher climate sensitivity in CMIP6. Geophys. Res. Lett. 47: e2019GL085782.
Ceppi P, Nowack P. 2021. Observational evidence that cloud feedback amplifies global warming. PNAS 118: e2026290118.

Energy balance + radiation.

Etminan M et al. 2016. Radiative forcing of carbon dioxide, methane, and nitrous oxide: A significant revision of the methane radiative forcing. Geophys. Res. Lett. 43: 12614-12623.
Meinshausen M et al. 2020. The shared socio-economic pathway (SSP) greenhouse gas concentrations and their extensions to 2500. Geosci. Model Dev. 13: 3571-3605.

Carbon cycle + budget.

Friedlingstein P et al. 2024. Global Carbon Budget 2024. Earth Syst. Sci. Data.
Saunois M et al. 2024. The Global Methane Budget 2000-2020. Earth Syst. Sci. Data.
Hugelius G et al. 2014. Estimated stocks of circumpolar permafrost carbon. Biogeosciences 11: 6573-6593.
Schuur EAG et al. 2022. Permafrost and climate change. Annu. Rev. Environ. Resour. 47: 343-371.
Gatti LV et al. 2021. Amazonia as a carbon source linked to deforestation and climate change. Nature 595: 388-393.